For any three numbers D_inf < D_1 <= D in [0,1], the authors construct a bounded fractal string whose zeta function has paramorphic barrier D_inf, meromorphic abscissa D_1, and absolute convergence abscissa D.
Fractality and Lapidus zeta functions at infinity
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abstract
We study fractality of unbounded sets of finite Lebesgue measure at infinity by introducing the notions of Minkowski dimension and content at infinity. We also introduce the Lapidus zeta function at infinity, study its properties and demonstrate its use in analysis of fractal properties of unbounded sets at infinity.
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math-ph 1years
2019 1verdicts
CONDITIONAL 1representative citing papers
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Essential singularities of fractal zeta functions
For any three numbers D_inf < D_1 <= D in [0,1], the authors construct a bounded fractal string whose zeta function has paramorphic barrier D_inf, meromorphic abscissa D_1, and absolute convergence abscissa D.